151 research outputs found

    High performance Python for direct numerical simulations of turbulent flows

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    Direct Numerical Simulations (DNS) of the Navier Stokes equations is an invaluable research tool in fluid dynamics. Still, there are few publicly available research codes and, due to the heavy number crunching implied, available codes are usually written in low-level languages such as C/C++ or Fortran. In this paper we describe a pure scientific Python pseudo-spectral DNS code that nearly matches the performance of C++ for thousands of processors and billions of unknowns. We also describe a version optimized through Cython, that is found to match the speed of C++. The solvers are written from scratch in Python, both the mesh, the MPI domain decomposition, and the temporal integrators. The solvers have been verified and benchmarked on the Shaheen supercomputer at the KAUST supercomputing laboratory, and we are able to show very good scaling up to several thousand cores. A very important part of the implementation is the mesh decomposition (we implement both slab and pencil decompositions) and 3D parallel Fast Fourier Transforms (FFT). The mesh decomposition and FFT routines have been implemented in Python using serial FFT routines (either NumPy, pyFFTW or any other serial FFT module), NumPy array manipulations and with MPI communications handled by MPI for Python (mpi4py). We show how we are able to execute a 3D parallel FFT in Python for a slab mesh decomposition using 4 lines of compact Python code, for which the parallel performance on Shaheen is found to be slightly better than similar routines provided through the FFTW library. For a pencil mesh decomposition 7 lines of code is required to execute a transform

    Efficient Solution of Large-Scale Algebraic Riccati Equations Associated with Index-2 DAEs via the Inexact Low-Rank Newton-ADI Method

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    This paper extends the algorithm of Benner, Heinkenschloss, Saak, and Weichelt: An inexact low-rank Newton-ADI method for large-scale algebraic Riccati equations, Applied Numerical Mathematics Vol.~108 (2016), pp.~125--142, doi:10.1016/j.apnum.2016.05.006 to Riccati equations associated with Hessenberg index-2 Differential Algebratic Equation (DAE) systems. Such DAE systems arise, e.g., from semi-discretized, linearized (around steady state) Navier-Stokes equations. The solution of the associated Riccati equation is important, e.g., to compute feedback laws that stabilize the Navier-Stokes equations. Challenges in the numerical solution of the Riccati equation arise from the large-scale of the underlying systems and the algebraic constraint in the DAE system. These challenges are met by a careful extension of the inexact low-rank Newton-ADI method to the case of DAE systems. A main ingredient in the extension to the DAE case is the projection onto the manifold described by the algebraic constraints. In the algorithm, the equations are never explicitly projected, but the projection is only applied as needed. Numerical experience indicates that the algorithmic choices for the control of inexactness and line-search can help avoid subproblems with matrices that are only marginally stable. The performance of the algorithm is illustrated on a large-scale Riccati equation associated with the stabilization of Navier-Stokes flow around a cylinder.Comment: 21 pages, 2 figures, 4 table

    Incorporating nodal and zonal room air models into building energy calculation procedures

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    Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2002.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 105-111).by Brent T. Griffith.S.M

    A study on block flexible iterative solvers with applications to Earth imaging problem in geophysics

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    Les travaux de ce doctorat concernent le développement de méthodes itératives pour la résolution de systèmes linéaires creux de grande taille comportant de nombreux seconds membres. L’application visée est la résolution d’un problème inverse en géophysique visant à reconstruire la vitesse de propagation des ondes dans le sous-sol terrestre. Lorsque de nombreuses sources émettrices sont utilisées, ce problème inverse nécessite la résolution de systèmes linéaires complexes non symétriques non hermitiens comportant des milliers de seconds membres. Dans le cas tridimensionnel ces systèmes linéaires sont reconnus comme difficiles à résoudre plus particulièrement lorsque des fréquences élevées sont considérées. Le principal objectif de cette thèse est donc d’étendre les développements existants concernant les méthodes de Krylov par bloc. Nous étudions plus particulièrement les techniques de déflation dans le cas multiples seconds membres et recyclage de sous-espace dans le cas simple second membre. Des gains substantiels sont obtenus en terme de temps de calcul par rapport aux méthodes existantes sur des applications réalistes dans un environnement parallèle distribué. ABSTRACT : This PhD thesis concerns the development of flexible Krylov subspace iterative solvers for the solution of large sparse linear systems of equations with multiple right-hand sides. Our target application is the solution of the acoustic full waveform inversion problem in geophysics associated with the phenomena of wave propagation through an heterogeneous model simulating the subsurface of Earth. When multiple wave sources are being used, this problem gives raise to large sparse complex non-Hermitian and nonsymmetric linear systems with thousands of right-hand sides. Specially in the three-dimensional case and at high frequencies, this problem is known to be difficult. The purpose of this thesis is to develop a flexible block Krylov iterative method which extends and improves techniques already available in the current literature to the multiple right-hand sides scenario. We exploit the relations between each right-hand side to accelerate the convergence of the overall iterative method. We study both block deflation and single right-hand side subspace recycling techniques obtaining substantial gains in terms of computational time when compared to other strategies published in the literature, on realistic applications performed in a parallel environment

    Parallel iterative methods in semiconductor device modelling

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    Automated Evaluation of One-Loop Six-Point Processes for the LHC

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    In the very near future the first data from LHC will be available. The searches for the Higgs boson and for new physics will require precise predictions both for the signal and the background processes. Tree level calculations typically suffer from large renormalization scale uncertainties. I present an efficient implementation of an algorithm for the automated, Feynman diagram based calculation of one-loop corrections to processes with many external particles. This algorithm has been successfully applied to compute the virtual corrections of the process uuˉbbˉbbˉu\bar{u}\to b\bar{b}b\bar{b} in massless QCD and can easily be adapted for other processes which are required for the LHC.Comment: 232 pages, PhD thesi

    Quantifying the forces in stabbing incidents

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    Stab wounds are an increasingly common cause of death or series injury and the high-risk groups in society are growing both in size and number. These facts make the study of mechanics of knife penetration more relevant than ever. The aim was to quantify the penetration force needed to inflict a certain stab wound by modelling knife penetration via the Finite Element Method. Case studies of stabbing incidents were carried out to give some insight into the nature and type of problem to be modelled. It was decided to work with an idealised stab-penetration model including a section of target tissue simulants. This stab-penetration test could yield repeatable and comparable results both experimentally and computationally. Suitable target simulants were identified by the stab-penetration test and also by uniaxial tensile tests. Pig skin was found to roughly match the mechanical properties of human skin with gelatine as a realistic flesh simulant. Computational modelling of knife penetration was attempted by use of Abaqus/Explicit, a nonlinear FEA package which features modelling of contact-impact problems. A true to scale finite element model of the stab-penetration test set-up was built including a material model of the target simulant. The computed penetration force was found highly mesh dependent for sharp blades and too high forces were predicted. Blunt penetrators were also tested both by experiments and computationally. By refining the constitutive model for skin computed values were obtained in reasonable agreement with the experiments for blunt penetrators. Mesh dependency was minimal in the computational model with blunt penetrators. It was concluded that modelling of knife penetration via finite element method is possible but analysis is time consuming due to the high mesh refinement required. Accuracy of the predicted penetration force is still too low for typical blade sharpnesses to be of practical use
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